Skin depth compensation for an in-ground transmitter

ABSTRACT

In a system in which a transmitter is moved through the ground in a region which includes an electrical conductivity characteristic and the transmitter transmits a locating signal for reception, compensating for skin depth error by measuring the locating signal such that measurements of the locating signal include skin depth error introduced as a result of the electrical conductivity characteristic. Thereafter, the measurements are used in a way which determines a skin depth corrected position of the transmitter. An associated compensation arrangement is also described.

RELATED APPLICATIONS

The present application is a continuation application of applicationSer. No. 11/281,969, filed on Nov. 16, 2005 now U.S. Pat. No. 7,327,144;which is a continuation application of application Ser. No. 10/822,123,filed on Apr. 10, 2004 and issued as U.S. Pat. No. 7,015,697 on Mar. 21,2006; which is a divisional application of application Ser. No.10/007,351, filed Nov. 7, 2001 and issued as U.S. Pat. No. 6,756,783 onJun. 29, 2004; which is a Continuation-In-Part of application Ser. No.09/854,036 filed May 14, 2001 that is now abandoned; which is acontinuation application of application Ser. No. 09/323,722 filed Jun.1, 1999 and issued as U.S. Pat. No. 6,285,190 on Sep. 4, 2001; thedisclosures of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

The present invention is related generally to the field of locatingand/or guiding an underground boring tool using a locating signal whichis transmitted through the ground and, more particularly, to a methodand associated apparatus for locating and/or guiding the boring tool ina way which compensates for skin effect that potentially introduceserror in locating and/or guiding the boring tool as a result ofconductivity of the earth through which the locating signal passes. Amulti-frequency locating system is introduced including highlyadvantageous transmitter and locator configurations. A highlyadvantageous tone detection arrangement is also introduced.

Referring to FIG. 1, boring tools are typically guided or located bytransmitting a dipole field from a dipole transmitter which ispositioned within the drill head of the boring tool. The locating/dipolefield is an oscillating signal that is generally emitted from a dipoleantenna oriented along the rotational axis of the drill head. FIG. 1illustrates a coordinate system including x, y and z axes with a dipoletransmitter D at its origin. For a point p, at a radius r from theorigin, the dipole equations are given as:

$\begin{matrix}{B_{x} = \frac{{3x^{2}} - r^{2}}{r^{5}}} & (1) \\{B_{y} = \frac{3{xy}}{r^{5}}} & (2) \\{{B_{z} = \frac{3{xz}}{r^{5}}},{and}} & (3) \\{r^{2} = {x^{2} + y^{2} + z^{2}}} & (4)\end{matrix}$Where B_(x), B_(y) and B_(z) represent orthogonal components of thedipole field at point p. The dipole equations are recited herein for thebenefit of the reader since these equations form a fundamental basis forthe use of a dipole field in locating applications. One such locatingsystem is described, for example, in U.S. Pat. No. 5,337,002 which iscommonly assigned with the present application. Traditionally, boringtool systems have not used compensation for conductivity of the soileven though this conductivity introduces a phenomenon commonly referredto as skin effect. While skin effect can result in significant locatingerrors, applicants submit that prior art systems have not provided suchcompensation, at least in part, since it is perceived in the art thatcompensation for skin effect is an extremely complex proposition.

What prior art system designers have generally done is to altogetherignore skin effect. This is tantamount to an assumption of anon-conducting earth. Accordingly, the electromagnetic field emitted bythe magnetic dipole of a transmitter into a non-conducting medium (suchas air) is described mathematically by the well known cubic law of amagnetic dipole (see FIG. 1). Unfortunately, however, as a direct resultof skin depth, drilling in the earth can produce significant deviationsfrom the cubic law when a typical oscillating magnetic dipole field isused. The latter term describes a magnetic dipole having a signalstrength that varies sinusoidally with time.

The present invention provides a highly advantageous and heretoforeunseen method and associated apparatus which provide compensation forskin effect in underground boring tool applications.

SUMMARY OF THE INVENTION

As will be described in more detail hereinafter, there are disclosedherein arrangements, apparatus and associated methods for skin depthcompensation in underground boring applications. Accordingly, in anoverall method of operating a system in which a boring tool is movedthrough the ground in a region which includes an electrical conductivitycharacteristic and where the system includes an above ground arrangementfor tracking the position of and/or guiding the boring tool as theboring tool moves through the ground and in which the system isconfigured for transmitting a locating signal between the boring tooland the arrangement in the region, the improvement comprisescompensating for skin depth error by measuring the locating signal suchthat measurements of the locating signal include skin depth errorintroduced as a result of the electrical conductivity characteristicand, thereafter, using the measurements in a way which determines a skindepth corrected position of the boring tool.

In one aspect of the invention a multi-frequency approach is providedwhich utilizes measured intensities of the locating field at two or morefrequencies to extrapolate a zero frequency value of locating signalintensity. The zero frequency value of intensity is then used inposition determination. The multi-frequency approach may be used inconjunction with walk-over type locators or with one or more aboveground receivers designed for receiving the locating signal at fixedposition(s). In one feature, the multi-frequency approach of the presentinvention does not require knowledge of earth properties or groundsurface geometry. The components of the measured magnetic fieldintensities of the locating field measured at their selected frequenciescontain property and geometry effects and pass them on to extrapolatedzero frequency values.

In another aspect of the invention, certain intensity measurements ofthe locating signal are used to determine a value for skin depth to beused during subsequent drilling, these certain measurements beingobtained in a calibration procedure by transmitting the locating signalfrom the boring tool on the surface of the ground to the above groundarrangement prior to drilling.

In still another aspect of the invention, a determined value of skindepth is used in one locating scenario with a walkover detector in whichthe walkover detector is used to establish an overhead position directlyabove the boring tool using a locating signal transmitted at a singlefrequency. The measured overhead signal strength of the locating signaltransmitted from the boring tool is then used in conjunction with thedetermined value of the skin depth to determine the depth of the boringtool below the overhead position on the surface of the ground such thatthe depth of the boring tool is established based at least in part onthe skin depth.

In another locating scenario, with the locating signal transmitted at asingle frequency, the boring tool moves through the ground along anintended path while transmitting the locating signal and moves in anorientation which includes pitch. The boring tool includes pitch sensingmeans and the locating signal exhibits a field defined forward point atthe surface of the ground with the boring tool at a particular pointalong the intended path. The field defined forward point beingvertically above an inground forward point on the intended path throughwhich the boring tool is likely to pass. The boring tool is located byusing a walkover detector to receive electromagnetic data whichidentifies the forward point. Signal strength of the locating signal isthen measured at the forward point, as transmitted from the boring toolat the particular point, and the measured signal strength of thelocating signal is used at the forward point in conjunction with thedetermined value of the skin depth and a sensed pitch value to determinethe depth of the boring tool referenced to the particular point and todetermine a forward distance on the intended path from the particularpoint at which the boring tool is located to the in-ground forwardpoint.

Alternatively, the field defined forward point may be located on orimmediately above the surface of the ground and an overhead point may beidentified on or immediately above the surface of the ground directlyabove the boring tool at the particular point. The forward distance ismeasured between the overhead point and the forward point as, defined atthe surface of the ground. Using the forward distance, the determinedvalue of skin depth and certain characteristics of the locating signalat the forward point, a skin depth corrected depth of the boring tool atthe particular point is determined.

In another alternative, the intended path of the boring tool in theregion is configured such that the forward point is at a higherelevation on the surface of the ground than the particular point. Theactual depth of the boring tool is then established at the particularpoint and a vertical elevation difference is measured between theparticular point and the forward point. Thereafter, the locating signalis sensed at the forward point while the boring tool is at theparticular point to determine an uncorrected depth of the boring toolwhich is subject to skin depth error. Using the measured verticalelevation difference, the actual depth of the boring tool at theparticular point and the uncorrected depth of the boring tool measuredfrom the forward point, a forward point skin depth correction factor isdetermined. During subsequent drilling operations the forward point skindepth correction factor is used in determining skin depth correcteddepth with the boring tool at subsequent particular points.

In another aspect of the invention, using a system in which a boringtool is moved underground in a region during selective rotation of theboring tool, the boring tool is configured with a transmitter fortransmitting a locating signal for use in tracking an undergroundposition of the boring tool in the region and for changing at least onecharacteristic of the locating signal responsive to subjecting theboring tool to a predetermined roll sequence during undergroundoperation. The predetermined roll sequence includes the steps ofrotating the boring tool for one time period at a first roll rate intimed relation to rotating the boring tool for another time period at asecond roll rate, followed by a halt in rotation. In one feature, thecharacteristic is the frequency of the locating signal. In anotherfeature, the characteristic is the power of the locating signal.

In still another aspect of the invention, a transmitter, configured forinstallation in a boring tool, includes a first arrangement fortransmitting a locating signal at a selected one of at least twofrequencies. A frequency selection arrangement, cooperating with thefirst arrangement, determines the selected one of the frequencies based,at least in part, on a pitch orientation of the transmitter. In onefeature, the frequency selection arrangement determines the selected oneof the frequencies responsive to the pitch orientation of thetransmitter upon power-up of the transmitter. In another feature, thefrequency selection arrangement is configured for detecting a pitchorientation sequence to which the transmitter is subjected. Responsiveto the detected pitch orientation sequence, the locating signalfrequency is changed.

In yet another aspect of the invention, a transmitter configured forinstallation in a boring tool includes a first arrangement fortransmitting a locating signal having a selected one of at least twofrequencies for use in tracking the boring tool and a frequencyselection arrangement, cooperating with the first arrangement, fordetecting the selected one of the frequencies as a power-down frequencyat a time when the transmitter is switched from an operational state toan off state and for restarting the first arrangement at the power-downfrequency upon switching from the off state to the operational state.

In a further aspect of the invention, a locator for receiving thelocating signal is configured for receiving the locating signal at anyselected one of the locating frequencies for use in tracking the boringtool. A control arrangement, forming part of the locator, detects theselected one of the frequencies as a power-down locating frequency at atime when the locator is powered down and, thereafter, powers up thelocator at least initially configured for receiving the power-downlocating frequency.

In another aspect of the invention, the system includes a locator fortracking the position of and/or guiding the boring tool as the boringtool moves through the ground. The boring tool includes a transmitterwhich transmits a locating signal at a selected one of at least twofrequencies for use in tracking the boring tool. The locator, in turn,receives the locating signal. The selected frequency of the locatingsignal is indicated to the locator by the boring tool using a frequencycontrol arrangement which forms part of the transmitter. In oneimplementation, a frequency indication is encoded on a carrier, whichcarrier is also used in determining the depth of the boring tool. Inanother implementation, the frequency indication is encoded on a carrierwhich is distinct from another carrier that is used in the boring tooldepth determination.

In still another aspect of the invention, in a system in which a boringtool is moved through the ground in a region including a locatingarrangement for tracking the position of and/or guiding the boring toolas the boring tool moves through the ground, the locating arrangementincludes a transmitter forming part of the boring tool for transmittinga locating signal at a selected one of at least two locating frequenciesand for transmitting a frequency designation identifying the selectedlocating frequency of the locating signal. A locator is included in thesystem configured for receiving the locating signal for use in trackingthe boring tool and itself including a frequency tracking arrangementfor switching the locator between different ones of the locatingfrequencies based on the frequency designation.

In a further aspect of the invention, a tone decoder is disclosed fordecoding an incoming analog data stream containing at least one tone.The incoming analog data stream is converted to a binary data streambased on one switching threshold. The binary data stream is then sampledover a sample period to establish a plurality of samples, each of whichis characterized as a binary value, at a rate based on the tone. Thesamples are used in a way which establishes at least an approximatemagnitude of the tone for the sample period. In one feature, alternatingones of the samples are used in contributing to a first value and asecond value such that the first value and the second value arecooperatively indicative of at least the approximate magnitude of thetone.

In another aspect of the invention, a tone detection arrangement isdisclosed for decoding an incoming data stream that is received insequential bit times and which incoming data stream contains at leastone tone that is selectively present for the duration of each bit time.A plurality of digital filters forms part of the detection arrangement,each of which is tuned for detecting the tone over a filter intervalthat is at least approximately equal in duration to the bit time from afilter start time to a filter stop time. A first one of the digitalfilters is started at a first start time in relation to a particular bittime. An additional one of the digital filters is started at anadditional start time which occurs following a predetermined intervalafter said start time of the first digital filter such that a number ofthe predetermined intervals at least approximately equals the bit timein duration. At the filter stop time of the first digital filter, atleast an approximate magnitude of the tone is determined for the filterinterval of the first digital filter. At the filter stop time of theadditional digital filter, at least the approximate magnitude of thetone is determined for the additional filter interval of the additionaldigital filter. In one feature, the filters are successively started andrestarted in a staggered timed relation such that one filter outputs theapproximate magnitude of the tone at a repeating interval correspondingto the predetermined interval at which the filters are started andrestarted.

In yet another aspect of the invention, a tone detection arrangementdecodes an incoming data stream which contains at least one tone that isselectively present. The tone detection arrangement includes a pluralityof digital filters each of which is tuned for detecting the tone over afilter interval from a filter start time to a filter stop time. Thedigital filters are started in a staggered time relation with respect toone another so as to operate over a plurality of intervals that are insaid staggered time relation with respect to one another including aplurality of said filter stop times which conclude the filter intervalsin the staggered time relationship. An average magnitude of the tone isdetermined responsive to the filter stop time of each filter.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention may be understood by reference to the followingdetailed description taken in conjunction with the drawings brieflydescribed below.

FIG. 1 is a diagrammatic illustration of a coordinate system forpurposes of describing the well know magnetic dipole equations.

FIG. 2 is a diagrammatic elevational view of a horizontal drillingoperation being performed in a region of ground using a portablewalkover detector, shown here to illustrate the effects of skin depth onlocating the boring tool.

FIG. 3 is a diagrammatic elevational view of another horizontal drillingoperation being performed in a region of ground using a portablewalkover detector, shown here to illustrate the effects of skin depth onlocating the boring tool with the walkover detector at a forward locatepoint.

FIG. 4 is diagrammatic elevational view of still another horizontaldrilling operation being performed in a region of ground using alocating/tracking system including fixed position above ground locatingfield detectors, shown here to illustrate the effects of skin depth onlocating the boring tool in a system using such fixed position aboveground locating field detectors.

FIG. 5 is a plot of transverse and radial absorption parameters againstthe ratio of range to skin depth, shown here to illustrate the nature ofthese absorption parameters with increasing range to skin depth ratios.

FIG. 6 is a plot of absorption parameters versus the ratio of range toskin depth for rich agricultural earth extending to infinity in alldirections, shown here to illustrate selected points on the absorptionparameters for use in validating the multi-frequency approach of thepresent invention.

FIG. 7 is a block diagram illustrating a multi-frequency transmittermanufactured in accordance with the present invention and suitable foruse in a boring tool.

FIG. 8 is a block diagram illustrating a multi-frequency receivermanufactured in accordance with the present invention and suitable foruse in a portable walkover detector or fixed position detector.

FIG. 9 is a perspective view of the surface of the ground on which acalibration procedure is being performed for determination of skin depthin accordance with the present invention using a portable walkoverdetector.

FIG. 10 is a plot illustrating a two point calibration function F.

FIG. 11 is a diagrammatic elevational view of an overhead positiondetermination setup, illustrating the determination of a skin depthcorrected depth of the boring tool.

FIG. 12 is a plot representing the deviation from the cubic law obtainedfrom a curve fit of Wait's theoretical results valid for a semi-infiniteconductive region and zero transmitter pitch in the range 0≦D/δ<3.

FIG. 13 is a diagrammatic elevational view of a forward locate positiondetermination setup, shown here to illustrate determination of a skindepth corrected depth of the boring tool from the forward locate point.

FIG. 14 is a diagrammatic elevational view of a surface offset distanceposition determination shown here to illustrate a variation in which anabove ground measurement between the forward locate point and anoverhead point directly above the boring tool is used in determining theskin depth corrected depth of the boring tool.

FIG. 15 is a diagrammatic elevational view of an above ground elevationoffset distance position determination setup, shown here to illustratestill another variation in which a forward locate point skin depthcorrection factor is developed for use in subsequent drillingoperations.

FIG. 16 is a diagrammatic elevational view of a dual point commonelevation position determination setup, shown here to illustrate the useof two identifiable points having a substantially common elevation.

FIG. 17 is a flow diagram illustrating one implementation of a locatingfrequency command sensing and update method in accordance with thepresent invention.

FIG. 18 is a block diagram of one configuration of a multi-frequencyreceiver produced in accordance with the present invention.

FIG. 19 is a block diagram of one possible implementation of aroll/pitch receiver forming part of the receiver of FIG. 18 shown hereto illustrate details of its configuration.

FIG. 20 is a flow diagram illustrating one implementation of a digitalmatch filter in accordance with the present invention for use in tonedetection used in the roll/pitch receiver of FIG. 19.

FIG. 21 is a diagrammatic plot showing in-phase and quadraturecomponents used in determining the approximate magnitude of a toneimplemented as used in the roll/pitch receiver of FIG. 19.

FIG. 22 is a diagrammatic plot illustrating the operation of a pluralityof digital match filters operating in staggered time relation withrespect to one another for use in tone detection in accordance with thepresent invention.

DETAILED DESCRIPTION OF THE INVENTION

Attention is immediately directed to FIG. 2 which illustrates a boringsystem operating in a region 12. It is noted that like reference numbersare used to refer to like components wherever possible throughout thevarious figures. The surface of the ground is indicated by the referencenumber 14. System 10 includes a boring tool 16 that is positioned on theend of a drill string 18 which is only partially shown. Boring tool 16includes a dipole transmitter 20 having an antenna 22 that transmits adipole locating field 24. The latter is received using a walkoverportable locator/detector 30. Specific details regarding theimplementation of system 10, as well as details regarding theimplementation of other types of systems in accordance with the presentinvention will be given at appropriate points hereinafter. For themoment, discussions will be limited to more general details regardingskin effect as related to the operation of system 10 in order tofacilitate the reader's understanding.

Still referring to FIG. 2, locating field 24, emitted by antenna 22 intoa non-conducting medium (not shown) such as air is describedmathematically by the cubic law, as mentioned above. However, drillingtakes place in the earth such as, for example, in region 12 which isassumed to possess electrical conductivity characteristics. Thesecharacteristics result in significant deviations from the cubic law whenlocating field 24 varies sinusoidally in time at a frequency f. Withconductivity of region 12 denoted as σ, the penetration distance oflocating field 24 as well as the shape of the magnetic field lines whichmake up the field depend on the frequency and conductivity parameters.Penetration distance is often called skin depth and is defined as:

$\begin{matrix}{\delta = \frac{1}{\sqrt{\pi\; f\;\mu\;\sigma}}} & (5)\end{matrix}$where μ denotes the permeability of the earth and δ is the skin depth.Thus, skin depth decreases if conductivity, σ, permeability, μ, orfrequency, f, increase. Conversely, skin depth becomes infinite at zerofrequency or conductivity, in which case the magnetic field is againdescribed by the magnetic dipole relationship. The significance of thezero frequency characteristics will become apparent at an appropriatepoint below. Increasing conductivity and/or frequency serve to weakenthe magnetic flux intensity recorded by locator 30 above ground. If skineffect is not accounted for, the boring tool can appear to be at aposition farther from the detector than in actuality. In the presentexample, where measurements are being taken with a walk-over locatordirectly over the drill head (OH), the transmitter can appear deeper, atposition A, where the boring tool is shown in phantom.

Referring now to FIG. 3, system 10 is shown once again with locator 30at a different position. Specifically, the locator is shown at what isreferred to as a forward negative locate point (FNLP) or, more simply,forward locate point (FLP) (see, for example, above referenced U.S. Pat.No. 5,337,002). An “X” is indicative of the configuration of thereceiving antenna within locator 30. At the FLP, the flux lines of thelocating field are characteristically vertically oriented. In theabsence of skin depth compensation, when the locator is at the forwardlocate point, dipole transmitter 22 can appear deeper and shiftedfarther away from the locator at position B where the boring tool isshown in phantom.

U.S. Pat. No. 6,035,951, filing date Apr. 16, 1997, entitled Systems,Arrangements and Associated Methods for Tracking and/or Guiding anUnderground Boring Tool is commonly assigned with the presentapplication and is incorporated herein by reference. One example of ahighly advantageous locating/guidance system conforming with the subjectapplication is shown in FIG. 4 and is generally indicated by thereference number 40. System 40 uses one or more above ground detectors42 positionable at fixed locations within region 12 for reception oflocating signal 24. With regard to the present application, skin depthproduces an effect in system 40 which is similar to that described withreference to FIG. 3. That is, boring tool 16 appears (shown in phantom)to be at position C at a deeper depth and shifted away from detectors42.

In some prior art systems, an above ground calibration procedure (notshown) is performed in an attempt to measure the signal strength of thedipole transmitter to be used in the boring tool with no considerationof the influence of skin effect. For example, the dipole transmitter andthe locator are placed on the surface of the ground at a knownseparation and orientation. In this regard, it is recognized herein thatskin depth has an effect on signal strength when such a calibrationprocedure is performed. Moreover, the skin effect in this above groundprocedure varies from the skin effect encountered when the boring toolis beneath the surface, which further complicates provisions for skindepth compensation. The accuracy of skin depth obtained from an aboveground calibration depends to a great extent on the homogeneity of thesoil. Skin depth will be accurate if the conductivity of the soil nearground surface, where the calibration has been performed, is similar tothat of the soil above the transmitter. Specifically, in the calibrationprocedure for ranges up to about three times skin depth, skin effectcauses an increase in recorded strength of the transverse component offlux intensity and hence the distance between transmitter and receiverappears smaller while an opposite trend can be observed for the radialcomponent of the flux intensity.

Having generally described the influence of skin depth, attention is nowdirected to details concerning provisions for effective compensation.The discussion immediately above, concerning an above ground calibrationprocedure, evidences that each component of the magnetic flux intensityis affected differently by earth conductivity and dipole frequency. Anexact solution, available for the components of magnetic flux intensityof a magnetic dipole immersed in homogenous earth (i.e., having auniform conductivity) of infinite extent is given in U.S. Pat. No.4,710,708, issued to Rorden et al. Rorden, however, relies on thesolution only to show that skin effect can be ignored when the range ofinterest is significantly less than the skin depth. Accordingly, Rordenuses a locating frequency that is low enough (generally 1-100 Hz) toproduce a sufficiently high skin depth in equation 5 above to accomplishthis objective. The present invention, however, considers the use ofsuch low frequencies as unacceptable because common signal detectionhardware and sensors such as coil loops are more sensitive at higherfrequencies. Additionally, state of the art systems such as, forexample, systems 10 and 40 described above contemplate the use of thelocating signal as a carrier for the purpose of transmitting data toabove ground locations wherein the data are encoded upon the locatingsignal. Carrier frequencies in the range of 1-100 Hz limit datatransmission capabilities optimistically to rates in the range of only0.5 to 50 Hz according to the Nyquist criteria.

Referring to FIG. 5, transverse and radial absorption parameters areshown plotted against the ratio of range, r, to skin depth, δ, based onthe Rorden expressions for these values. Exponential decay is shown forcomparison. It is of interest here to note that Rorden fails to providea plot such as that of FIG. 5 and, even though Rorden lists theequations, he fails to observe that the transverse and radial componentsare each affected in a different way as r/δ increases. Both components,however, approach exponential decay asymptotically for large values ofr/δ. At the same time, it is important to understand that the usefulnessof the Rorden teachings is inherently limited, in a practical sense,because the presence of a ground surface is not modeled. As will beseen, the present invention resolves the difficulties in using locatingsignals having frequencies sufficiently high for providing ease ofdetection and adequate data transfer rates using the locating signal asa carrier while providing effective and highly advantageous compensationfor skin effect, even though the locating frequencies used are highenough to encounter levels of skin effect that should not be ignored.

In one implementation of the present invention, which is applicable toessentially any underground boring system including systems 10 and 40described above, the recognition must be emphasized that the locatingfield is governed by the cubic law of a magnetic dipole if the signalfrequency goes to zero, because the skin depth goes to infinityregardless of the conductivity of the earth. At first blush, thisrecognition may seem of little importance to one of ordinary skill inthe art since, as a practical matter, static magnetic fields (i.e., atzero frequency) are useless in the present application. That is, only atime varying field is readily measurable with sensitive detectors suchas coils. However, the present invention overcomes the seeminguselessness of attempting a solution at zero frequency by providing ahighly advantageous multi-frequency approach which allows theformulation of a zero frequency solution. Moreover, the multi-frequencyapproach taken by the present invention may readily be implemented usingexisting technologies, as will be seen immediately hereinafter.

The multi-frequency approach of the method of the present inventionrequires transmission and reception of the locating field using at leasttwo different frequencies. While specific implementations to bedescribed rely on the use of four different frequencies, it is to beunderstood that any number of frequencies of two or more may beemployed. To some extent, it is considered that accuracy may beenhanced, however, when more than two frequencies are used. Detailsregarding frequency selection will be provided at an appropriate pointbelow. In the four frequency implementation under discussion,measurement of the locating field is made at one or more above groundlocations using either one or more detectors configured for use at fixedlocations and/or using a portable walkover locator. Receivers in eithera portable walkover locator or in fixed position above ground detectorsmay be configured in essentially the same manner, in accordance withthese teachings. During operation of any system utilizing themulti-frequency approach of the present invention, measurements are madeat the above ground locations corresponding to each of the selectedfrequencies. Thereafter, these measurements are utilized in a highlyadvantageous way which serves to extrapolate a zero frequencymeasurement. For example, it may be assumed for any particular aboveground location that the component of the magnetic field intensity ofthe locating signal measured at the i-th frequency f_(i) depends on skindepth according to:

$\begin{matrix}{S_{i} = {S_{0}{F\left( \frac{D}{\delta} \right)}}} & (6)\end{matrix}$where S₀ is a constant which corresponds to the intensity of thelocating field at zero frequency, δ_(i) is the skin depth at each of theselected frequencies, D is the depth or some characteristic length scaleof the boring tool and F is a function to be determined. Thus, theobjective is to establish the value of S₀ based on the values S_(i). Tothat end, for each of the selected frequencies, an interpolationpolynomial or any other suitable mathematical function including anexact solution, if obtainable, may be used to provide a curve fit to themeasured data for each of the frequencies. As an example, a cubicpolynomial can be used to approximate the function, F, at the fourrequired frequencies. Introducing the definition of skin depth, themagnetic field intensities can be written as:S ₁ =S ₀ +af ₁ ^(0.5) +bf ₁ +cf ₁ ^(1.5)  (7)S ₂ =S ₀ +af ₂ ^(0.5) +bf ₂ +cf ₂ ^(1.5)  (8)S ₃ =S ₀ +af ₃ ^(0.5) +bf ₃ +cf ₃ ^(1.5)  (9)S ₄ =S ₀ +af ₄ ^(0.5) +bf ₄ +cf ₄ ^(1.5)  (10)

Equations 7-10 are a set of linear equations for the unknowncoefficients S₀, a, b and c that can be solved employing standardsolution methods. It should be noted that this approach is veryefficient numerically, requiring a small matrix to be inverted withcoefficients depending on the chosen frequencies. Once a value for S₀ isobtained, the position of the boring tool can be determined using thewell known cubic equations 1-4 above. Remarkably, there is no need todetermine the skin depth values δ_(i). Since the selected frequenciesare chosen prior to initiation of drilling, the inversion of this matrixneed only be performed once. Other formulations of signal strength ateach frequency, S_(i), may be used. For example, one possibleformulation may be based on the exact solution of Rorden in whichexponential decay is observed for large values of r/δ, the equations maybe expressed in the form:

$\begin{matrix}{S_{i} = {S_{0}{\mathbb{e}}^{- \frac{r}{\delta_{i}}}{G\left( \frac{r}{\delta_{i}} \right)}}} & (11) \\{S_{i} = {{\mathbb{e}}^{- {cf}_{i}^{0.5}}\left( {S_{0} + {{af}_{i}}^{0.5} + {bf}_{i}} \right)}} & (12)\end{matrix}$where G is a function to be determined and all other values aredescribed above. It should be noted that this approximation alsorequires measurements at four frequencies but the four resultingequations for unknown coefficients S₀, a, b, c are nonlinear. Hence, thesolution method is somewhat less efficient than one based on polynomialapproximations, but remains applicable over a wider range of skin depth.Once again, there is no need to determine the values δ_(i).

Referring to FIG. 6, an important feature of the multiple frequencyapproach of the method of the present invention resides in the fact thatit does not require knowledge of earth properties or ground surfacegeometry. The components of the magnetic field measured at nonzerofrequencies contain property and geometry effects and pass them on toextrapolated zero frequency values. FIG. 6 demonstrates the validity ofthis approach for a simplified case, rich agricultural earth (i.e.,meaning higher conductivity soil) extending to infinity in alldirections. In this example, any variations of earth conductivity andthe effect of ground surface and air on the magnetic field areneglected. The transverse and radial absorption parameters, representingthe deviation of the magnetic field from the cubic law of magneticdipoles, are plotted vertically against the ratio of range to skin depthas dashed lines indicated by the reference numbers 50 and 52,respectively. Points 50 a-d and 52 a-d have been selected on eachabsorption parameter curve corresponding to transmitter frequencies of2, 8, 14 and 20 kHz, respectively. As seen, extrapolation of the curveusing the polynomial formulation of equations 7-10 provides magneticfield data that are within 2% of known exact values for the absorptionparameters at zero frequency (i.e., the known value of 1.0 for both ofthe absorption parameters at zero frequency). In the method of thepresent invention, the extrapolation is performed for magneticintensity, however, the present example serves to illustrate thevalidity of this approach even though the absorption parameters wereextrapolated since magnetic intensity is the product of the cubic lawand absorption parameter. Even though the discussion dealt withdistributed conductivity of soil, the multiple frequency approach willwork for other field distortions due to conductivity including but notlimited to buried electrical conductors, pipes, plates and rebar.

With regard to selection of frequencies at which the locating signal isto be transmitted, it is noted that an unlimited number of differentfrequency combinations may be employed. Since an extrapolation to zerofrequency is being performed, however, it is considered that thefrequencies should be as low as possible while still providing foradequate detection and transmission of data, using the locating signalas a carrier. For example, frequencies in the range of 2-40 kHz areconsidered as acceptable.

Referring now to FIG. 7, having described the multi-frequency approachof the method of the present invention, descriptions will now beprovided of components appropriate for use in systems which utilize theapproach. FIG. 7 illustrates a multi-frequency transmitter manufacturedin accordance with the present invention and generally indicated by thereference number 100. Transmitter 100 includes a sensor/conditioningsection 102 and a carrier generation/antenna drive section 104.Transmitter 100 is generally configured for use in a boring tool, incertain instances, the transmitter may be used in above groundapplications such as, for example, in a calibration and/or system testunit (not shown).

Still referring to FIG. 7, sensor/conditioning section 102 includes asuitable group of sensors in this instance comprising, for example, athree-axis gyro 106, a three-axis magnetometer 108, a three-axisaccelerometer 110, a roll/pitch sensor 112, a temperature sensor 114 anda battery sensing section 116. Physical parameters at the outputs ofmagnetometer 108, accelerometer 110 and roll/pitch sensor 112, as wellas the transmitter battery conditions using battery sensing section 116and temperature using temperature sensor 114, are provided to amultiplexer 118 which then transfers all of these signals in multiplexedform to an analog to digital converter 120. The latter digitizes andconverts the multiplexed signals into digital format, for example, ateither an 8-bit or 12-bit resolution, depending on accuracyrequirements. Thereafter, a microprocessor 122 processes all of theparameters provided from the analog to digital converter and convertsthe parameters into information relating to the in-ground transmittercoordinates or relating to down-hole conditions. For example, duringthis parameter processing, the microprocessor may perform linearizationand temperature compensation on the output of roll/pitch sensor 112 inorder to calculate an absolute pitch position of the boring tool. Thepitch output may further be compensated based on the determination of aparticular roll position. Linearization and compensation coefficientsare generated during factory calibration and stored in a calibrationconstant section 124 which comprises a non-volatile memory area withintransmitter 100. It is noted that programming of microprocessor 122 isconsidered to be within the ability of one having ordinary skill in theart in view of this overall disclosure.

Once the calculations are complete relating to all of the signals fromsensors in sensor/conditioning section 102, the results are transmittedto one or more above ground locations. To that end, carriergeneration/antenna drive section 104 includes an oscillator 126 whichprovides a clock signal to microprocessor 122 and to a divide by Ncounter 128. The latter receives a frequency select input frommicroprocessor 122 on an f select line 130 such that the divide by Ncounter may selectively generate any one of a wide range of carrierfrequencies. The carrier frequency may be selected by microprocessor 122under software control in a number of different ways. In oneconfiguration, frequency selection can be performed at the beginning ofthe drilling operation, for example, after monitoring of backgroundnoise levels at various frequencies such that noisy frequencies may beavoided. Such noisy frequencies may be attributed, for instance, totraffic loops, invisible dog fences, cable TV, and power lines in aparticular region. In another configuration, the transmitter may changefrequencies on the fly, after the drilling has started. On the flyfrequency change can be initiated either by the microprocessor using apre-determined algorithm, or by the request of the drilling operator,for example, using a signal transmitted by telemetry from the surface tothe boring tool or transmitted through the drill string using anisolated electrical conductor or based on possibilities such as, forexample, boring tool roll orientation sequence and roll rate.Particularly advantageous arrangements for automatically forming anisolated electrically conductive path between the drill rig and anin-ground device such as a boring tool to provide power and signal pathsare disclosed in co-pending U.S. patent application Ser. No. 09/317,308which is incorporated herein by reference.

The selected carrier frequency is then passed to a modulation section132 which is configured for modulating data from sensor/conditioningsection 102 onto the selected carrier frequency. Modulation section 132receives the data on a data line 134 from microprocessor 122 and alsoreceives a modulation selection signal on a mod select line 136connected with the microprocessor. The modulation selection signal mayselect, for example, phase modulation or amplitude modulation, orcombinations of both. The modulation scheme may be programmed eitherbefore or during the drill, much in the same manner as in the case ofthe carrier frequency, described above.

With continuing reference to FIG. 7, data modulation section 132 passesa modulated carrier signal to a driver section 140. The driver sectionreceives a power selection input on a power select line 142 frommicroprocessor 122. In this way, the output of transmitter 100 may betailored to drilling conditions, for example, to conserve battery powerin a shallow drill run or to increase transmitter output at longerranges and/or drilling depths or even to stop transmission altogetherduring idle periods of a drilling operation. Control of the power aswell as other functions can be achieved using procedures such as havebeen described for frequency control. The transmitter can send encodeddata (as is done for roll, pitch and other parameters) to allow thereceiver to adjust its calibration for the new signal strength. Thiswill allow the operator to continue monitoring depth or range withoutthe need to recalibrate while drilling. An antenna drive signal isproduced on an antenna line 144 which is coupled to an antenna 146 whichgenerally comprises a dipole antenna for emanation of locating signal24.

In accordance with the multi-frequency approach of the presentinvention, described above, transmitter 100 may alternately transmit oneof four selected carrier frequencies from the boring tool. The carrierfrequencies may alternate at any suitable rate such as, for example, 10Hz and may be selected in accordance with considerations describedpreviously. It should be appreciated that transmitter 100 is configuredfor flexibility in carrying out the method of the present invention.That is, fewer or more than four carrier frequencies may readily betransmitted either individually or simultaneously.

Turning now to FIG. 8, a multi-frequency receiver manufactured inaccordance with the present invention is generally indicated by thereference number 150. Locating signal 60 is received by an antennaarrangement 152 which may include three orthogonally arranged x, y and zantennas indicted by reference numbers 154, 156 and 158, respectively.The locating signal received by each antenna is first amplified byrespective very low noise pre-amplifiers 160 a-c prior to processing.This pre-amplification maintains the received signal-to-noise ratiowhile making any noise introduced by subsequent circuitry relativelynegligible. The amplified antenna signals (not shown) are then fed tomixers 162 a-c to be translated down to a lower intermediate frequency(IF). In this manner, any locating signal frequency within a suitabledesign range such as, for example, 2-40 kHz can be received throughappropriate adjustment of the frequencies of the mixers such thatoutputs of the mixers fall within a selected IF band.

Still referring to FIG. 8, the mixers are followed immediately bynarrow-band, band-pass filters 164 a-c which essentially pass only thelocating signals at the translated IF frequency. The IF frequency can beeither the sum or the difference of the carrier frequency and the mixerfrequency. The filtered x, y and z signals are further amplified byprogrammable-gain amplifiers (PGA's) 166 a-c before being received by ananalog-to-digital converter 168. PGA's 166 provide over 96 dB of dynamicrange and are each directly controlled by a digital signal processor(DSP) 170. One suitable DSP is the ADSP2185L, a sixteen bit fixed pointDSP manufactured by Analog Devices, Inc. Analog-to-digital converter(ADC) 168 digitizes the received signals, at a rate controlled by adirect digital synthesizer (DDS) 172 which is, in turn controlled by DSP170. The DSP and DDS receive an oscillator signal from an oscillator174. Using the oscillator signal and based on control from the DSP, theDDS generates a local oscillator frequency (LO) for mixers 162. The ADCdigitizes the received signals at the rate determined by the DDS andconverts the signals to a binary number two's complement format. Theconversion rate is either four times the IF frequency, if a quadraturesampling scheme is used, or may be significantly less than the IFfrequency, if an under-sampling scheme is chosen. The resolution of theADC may be 12-bit to 16-bit. All axes are simultaneously sampled inorder to maintain relative phase.

Continuing to describe receiver 150, digital signal processor DSP 170,controls all operations of the receiver including mixing frequency, PGAgain, and a selected signal processing algorithm. In the case of aquadrature sampling scheme, the DSP samples the received signals at fourtimes their IF (translated) frequency and then multiples the receivedsignals it by a separate Sine and Cosine sequence to obtain in-phase andquadrature-phase components. This process converts the received signalfrom its IF frequency down to a base-band frequency that containsmodulated data, if present, while, at the same time, breaks down thesignal into its in-phase (I) and quadrature-phase (Q) components. The Iand Q components are each passed through a simple low-pass filter (notshown) to remove everything but the modulated data. The filtered outputsare then used to obtain the original data as well as further processingto recover signal magnitude and sign information. Additionally, theoutputs are also used, along with a modified phase-lock-loop techniqueknown as Costas loop, for controlling the DDS frequency (which controlsthe mixer frequency and ADC sample rate) and the PGA gain settings. Theexact algorithm varies depending on the modulation scheme used but maybe developed by one having ordinary skill in the art in view of thisoverall disclosure.

If under sampling (not shown) is used, the DSP would sample the receivedsignals at a rate much lower than the IF frequency. The digitized datais then processed using a match filter to obtain data, magnitude, andsign information as well as for PGA gain control. Irrespective ofsampling, the DSP implementation is considered to be highlyadvantageous, resulting in a very flexible and adaptive multi-frequencyreceiver. Many modifications (not shown) are possible in view of thisdisclosure for purposes of performance improvement. For example, mixers162 can be eliminated by replacing narrow-band band-pass filters 164with broadband band-pass filters and using ADC 168 to perform quadraturesampling and direct-to-base-band conversion (digital mixing) in a singleoperation. In order to receive the locating signal at differentfrequencies, DSP 170 may either sample the data at different rates orsample everything at a single, fixed rate and then perform rateconversion in software using decimation and interpolation techniques(known as digital re-sampling). As mentioned previously, it should beappreciated that receiver 150 may readily be incorporated into either aportable walkover locator or into detectors designed for use at fixedpositions with a drilling region.

Having described a highly advantageous multi-frequency approach for usein skin depth compensation, skin depth compensation techniques using asingle frequency locating signal will now be described with regard to anumber of different exemplary scenarios. It is to be understood thatexisting systems using portable locators may readily be adapted inconformity with these teachings or, alternatively, new systems usingeither a portable locator and/or one or more locating field detectorsdesigned for positioning at fixed locations within a drilling region arealso readily adaptable in view of these teachings.

Referring now to FIG. 9, the techniques disclosed herein for use withsingle frequency locating signal transmission initially rely on adetermination of the skin depth in the drilling region. As mentionedpreviously, some prior art systems utilize an above ground calibrationprocedure in an attempt to relate the signal strength of a dipoletransmitter to distance without skin depth compensation. The presentinvention introduces a technique for performing an above groundcalibration procedure which not only provides dipole signal strength,but also yields a value for skin depth in the drilling region which maybe used in subsequent position determination techniques accounting forskin depth. FIG. 9 illustrates a calibration procedure being performedusing a portable walkover detector 260 in a region 262. The calibrationprocedure is performed on the surface of the ground which is assumed tobe planar for purposes of simplicity, having x and y coordinate axesdefined as shown. A dipole transmitter 264 is diagrammaticallyillustrated and is oriented along the y axis while being centered uponthe x axis. Preferably, the transmitter should be the transmitter whichis to be used during subsequent drilling operations in a drillingconfiguration such as housed in the drill head (not shown) placed on thesurface of the ground. Alternatively, the transmitter itself may bepositioned on the ground, but it must be remembered that measurementsare likely to be affected by any housing later positioned around thetransmitter.

Still referring to FIG. 9, the calibration procedure is performed withthe walkover locator at two offset positions along the x axis indicatedby the reference numbers 266 a, corresponding to an offset distance ofx1, and 266 b, corresponding to an offset distance of x2. Transmitter264 transmits locating signal 24 at a single frequency. It is to beunderstood that the calibration procedure may just as readily beperformed using a detector which is intended for location at a fixedposition within the drilling region following the calibration procedure.In this regard, irrespective of the specific form of the detectorinstrument to be used in the calibration procedure, the instrumentshould be positioned such that its locating field sensor arrangement ison the x axis. In the instance of a walkover locator having an antennaconfiguration as described, for example, in above referenced U.S. Pat.No. 5,337,002, which is commonly assigned with the present application,the plane of the antenna arrangement should be aligned parallel to the yaxis of the transmitter. In the instance of a locating field detectorincluding three orthogonal receiving axes, such as described in aboveincorporated U.S. Pat. No. 6,035,951 the detector arrangement issomewhat arbitrary since signals measured along the three axes can betransformed mathematically into any desired directions.

Using the configuration shown in FIG. 9, the calibration procedure isperformed by measuring the components of the magnetic flux intensityB_(y1) and B_(y2) at positions x₁ and x₂, respectively. Geophysicaltheory provides an equation for the calculation of dipole strength andskin depth that has the general form:B _(y) =B _(y)(x, y, m, δ)  (13)where B_(y) is a measured intensity, x and y are the coordinates of thelocator/detector, m is the signal strength of the dipole transmitter andδ is the skin depth. At this time, a preferred method is based on thetheory of Wait et al (Journal of Geophysical Research, Vol. 58, No. 2)which is valid for zero transmitter pitch, level ground surface andhomogeneous soil conditions, as are present in FIG. 7. Wait solvesMaxwell's equations with boundary conditions at the ground surfacecorrectly satisfied. Since the calibration procedure provides two valuesof magnetic flux intensity and the distances x₁ and x₂, two nonlinearequations for calculating m and δ are obtained:B _(y1) =B _(y)(x ₁,0,m,δ)  (14)B _(y2) =B _(y)(x ₂,0,m,δ)  (15)

The deviation of B_(y) from the cubic law is approximated in the range0<=x/δ<3 by:

$\begin{matrix}{{B_{y} = {\frac{m}{x^{3}}{F\left( \frac{x}{\delta} \right)}}},{and}} & (16) \\{{F\left( \frac{x}{\delta} \right)} = {1 + {b\frac{x}{\delta}} + {c\left( \frac{x}{\delta} \right)}^{2} + {d\left( \frac{x}{\delta} \right)}^{3}}} & (17)\end{matrix}$where the function F is shown in FIG. 10. The unknown coefficients b, cand d can be obtained from this graph using standard numericaltechniques.

Using equations 16 and 17, the following equations can be obtained whichcan be solved for m and δ:

$\begin{matrix}{B_{y\; 1} = {\frac{m}{x_{1}^{3}}\left\lbrack {1 + {b\frac{x_{1}}{\delta}} + {c\left( \frac{x_{1}}{\delta} \right)}^{2} + {d\left( \frac{x_{1}}{\delta} \right)}^{3}} \right\rbrack}} & (18) \\{B_{y\; 2} = {\frac{m}{x_{2}^{3}}\left\lbrack {1 + {b\frac{x_{2}}{\delta}} + {c\left( \frac{x_{2}}{\delta} \right)}^{2} + {d\left( \frac{x_{2}}{\delta} \right)}^{3}} \right\rbrack}} & (19)\end{matrix}$

The solution is obtained in 2 steps. First, the following variables aredefined after introduction in equations 18 and 19:

$\begin{matrix}{g_{1} = {B_{y\; 1}x_{1}^{3}}} & (20) \\{g_{2} = {B_{y\; 2}x_{2}^{3}}} & (21) \\{ɛ = \frac{1}{\delta}} & (22)\end{matrix}$

Subtracting equation 19 from equation 18 provides equation 23 for ε:(g ₁ x ₂ ³ −g ₂ x ₁ ³)dε ³+(g ₁ x ₂ ² −g ₂ x ₁ ²) cε ²+(g ₁ x ₂ −g ₂ x₁)bε+g ₁ −g ₂=0  (23)

Equation 23 can be solved employing a standard method such as Newton'sto yield δ. Thereafter, dipole strength, m, follows directly from:

$\begin{matrix}{m = \frac{B_{y\; 1}x_{1}^{3}}{1 + {b\frac{x_{1}}{\delta}} + {c\left( \frac{x_{1}}{\delta} \right)}^{2} + {d\left( \frac{x_{1}}{\delta} \right)}^{3}}} & (24)\end{matrix}$Thus, dipole signal strength, m, and skin depth, δ, are established foruse in subsequent position determinations.

Turning now to FIG. 11, in a first scenario, an overhead positiondetermination setup (hereinafter OH setup) is generally referred to bythe reference number 270 with a detector (not shown) at a position 272located directly overhead (hereinafter OH setup) of transmitter 264transmitting locating signal 24. At this location, the flux lines of themagnetic locating field are characteristically horizontal substantiallyover the transmitter. The detector measures the horizontal component ofthe magnetic flux intensity B_(x). With m and δ known from the foregoingabove ground calibration transmitter depth and with a measured value ofintensity,

$\begin{matrix}{B_{x\; D} + {B_{x}\left( {m,D,\frac{D}{\delta}} \right)}} & (25)\end{matrix}$B_(xD), from the detector, D, is determined from a single equationwritten symbolically as:

The exact form of equation 25 can either be obtained from geophysicaltheory or from dimensional analyis. Applying the latter (e.g., P. W.Bridgman, Dimensional Analysis, 1931) six variables are identifiedgoverning the physics of OH setup depth measurement. The variablesinclude B_(x), μ, σ, f, D and m which have been defined previously.Furthermore, four fundamental units including length, time, volt, andampere characterize the problem. Hence according to the π-theorem ofdimensional analysis six minus four or two non-dimensional groupsdescribe the OH setup measurements mathematically. The twonon-dimensional groups include

$\begin{matrix}\frac{B_{x}D^{3}}{m} & (26) \\{\mu\;\sigma\;{fD}^{2}} & (27)\end{matrix}$

The second group given by equation 27 can be simplified to D/δ using thedefinition of skin depth

$\begin{matrix}{B_{x} = {\frac{m}{D^{3}}{G\left( \frac{D}{\delta} \right)}}} & (28)\end{matrix}$equation 5. Hence B_(x) must be of the following general form:Here, the function G represents the deviation from the cubic lawobtained from a curve fit of Wait's theoretical results valid for asemi-infinite conductive and zero transmitter pitch in the range 0≦D/δ<3medium, shown in FIG. 12. Since this equation is nonlinear for depth D,an iterative procedure must be formulated. As one example:

$\begin{matrix}{D = \left( {\frac{m}{B_{x}}{G\left( \frac{D}{\delta} \right)}} \right)^{\frac{1}{3}}} & (29)\end{matrix}$

Function iteration/successive approximation is performed beginning withan initial guess for D, e.g. the value corresponding to infinite skindepth. In successive approximations, the procedure inserts the lastavailable value for D on the right hand side of this equation therebycalculating a new, more accurate value. This process is repeated untilchanges between successive values of D are reduced to a specifiedtolerance.

The analysis outlined immediately above provides the correct functionalrelation between variables governing OH setup depth measurement whichcan be written as:

$\begin{matrix}{{G\left( \frac{D}{\delta} \right)} = {\sum\limits_{i = 1}^{N}\;{c_{i}\left( \frac{D}{\delta} \right)}^{d_{i}}}} & (30)\end{matrix}$

The unknown coefficients c_(i) and d_(i) must be obtained from anothersource, for example, Wait's theory or a physical experiment conducted indifferent soil conditions and at various depths. Another method forobtaining these coefficients relies entirely on numerical modelingsolving Maxwell's equations and pertinent boundary conditions. Computercodes are commercially available to aid in this task such as, forexample, software by Infolytica Corporation in Montreal, Canada.

Attention is now directed to FIG. 13 which illustrates a second scenariorepresenting a Forward Locate Point position determination setupgenerally indicated by the reference numeral 290. It should be mentionedthat even though the present discussions are made with reference to theforward locate point, these concepts are equally applicable to the rearlocate point. In this instance, detector 30 measures the magnitude ofthe magnetic flux intensity B (not shown) as a result of locating signal24 transmitted from transmitter 264 within drill head 274. In addition,transmitter pitch γ is measured. In order to calculate transmitter depthfrom these measured quantities the following equations must be solved:

$\begin{matrix}{B_{\xi} = {B_{\xi}\left( {\xi,\eta,\frac{r}{\delta}} \right)}} & (31) \\{B_{\eta} = {B_{\eta}\left( {\xi,\eta,\frac{r}{\delta}} \right)}} & (32) \\{{\tan\;\gamma} = \frac{B_{\xi}}{B_{\eta}}} & (33) \\{D = {r\;{\sin\left( {\lambda + \gamma} \right)}}} & (34) \\{B_{y} = \sqrt{B_{\xi}^{2} + B_{\eta}^{2}}} & (35) \\{{\tan\;\lambda} = \frac{\xi}{\eta}} & (36) \\{r^{2} = {\xi^{2} + \eta^{2}}} & (37)\end{matrix}$

The definitions of the geometric variables D, r, ξ, η, λ are given inFIG. 13. It is noted that transmitter depth is the distance from theground surface to the transmitter. Since the locator antennas measuresignals above ground, the distance between the antennas and ground mustbe subtracted from the computed depth. These variables and the twocomponents of the magnetic field intensity B_(ξ) and B_(η) make up atotal of 7 unknowns that can be obtained from the listed seven equationsusing standard numerical methods. An example of a convenient solutionmethod is to rewrite the equations in terms of polar coordinates r, λusingξ=r cos λ  (38)η=r sin λ  (39)

This transformation eliminates two equations. The remaining equationsthen read:

$\begin{matrix}{B_{\xi} = {{B_{\xi}\left( {r,\lambda,\frac{r}{\delta}} \right)} = {\frac{{3\;\cos^{2}\lambda} - 1}{r^{3}}{H_{1}\left( \frac{r}{\delta} \right)}}}} & (40) \\{B_{\eta} = {{B_{\eta}\left( {r,\lambda,\frac{r}{\delta}} \right)} = {\frac{3\;\sin\;\lambda\;\cos\;\lambda}{r^{3}}{H_{2}\left( \frac{r}{\delta} \right)}}}} & (41) \\{{\tan\;\gamma} = \frac{B_{\xi}}{B_{\eta}}} & (42) \\{B_{y} = \sqrt{B_{\xi}^{2} + B_{\eta}^{2}}} & (43) \\{D = {r\;{\sin\left( {\lambda + \gamma} \right)}}} & (44)\end{matrix}$

Note that the equations for the components of magnetic field intensityexpress the cubic law of a magnetic dipole multiplied by a function H₁or H₂ that accounts for the effect of skin depth. The latter is knownfrom an above ground calibration, as described above. Details of thesefunctions can be derived employing either geophysical theory ordimensional analysis. Further, note that equation 44 for transmitterdepth is uncoupled from the other equations allowing independentsolution for the position coordinates r and λ of the FLP based on thefollowing nonlinear equations:

$\begin{matrix}{{{{B_{\eta}\left( {r,\lambda,\frac{r}{\delta}} \right)}\tan\;\gamma} - {B_{\xi}\left( {r,\lambda,\frac{r}{\delta}} \right)}} = 0} & (45) \\{{B_{y}^{2} - {B_{\xi}^{2}\left( {r,\lambda,\frac{r}{\delta}} \right)} - {B_{\eta}^{2}\left( {r,\lambda,\frac{r}{\delta}} \right)}} = 0} & (46)\end{matrix}$where the variables have been defined above. These equations can besolved employing any of the standard solution methods for sets ofnonlinear equations such as, for example, Newton's and functioniteration.

Turning now to FIG. 14, in a third scenario, a surface offset distanceposition determination setup is generally indicated by the referencenumber 320. This setup technique uses the FLP and OH points indicated bythe reference numbers 322 and 324, respectively. In this regard, it isnoted that the locations of these points are affected as a result ofskin depth. At forward locate point 322, the horizontal component,B_(x), of the magnetic flux intensity vanishes. This fact can be used toderive a formula for transmitter depth D as a function of a horizontaldistance, Δx_(G), at the surface of the ground between OH point 324 andFLP 322. In applications where skin effect can be neglected, a simpleequation for depth, D, can be derived from the cubicD=√{square root over (2)}Δx_(G)  (47)law for a dipole field:

In order to account for skin effect relying on B_(x)=0, a different formof the equation is used which is written in symbolic notation as:

$\begin{matrix}{{B_{x}\left( {\frac{r}{\delta},{\Delta\; x_{G}},D} \right)} = 0} & (48)\end{matrix}$Here, skin depth δ is obtained from an above ground two-pointcalibration as described earlier and Δx_(G) can be measured easily usingavailable standard distance measurement methods. Details of thisequation can also be derived from geophysical theory, e.g., theaforementioned work published by Wait. In general, an explicit formulafor depth cannot be derived from this equation since it will most likelybe nonlinear in D, therefore, the expression must be solved numericallyemploying a suitable standard solution method such as Newton's orfunction iteration.

Attention is now directed to FIG. 15 which illustrates a fourth, aboveground elevation offset distance position determination setup generallyindicated by the reference number 360. This setup technique is useful inconjunction with an OH measurement of drill head depth, D_(OHδ), whichaccounts for skin depth such as, for example, described above in the OHposition determination setup associated with FIG. 11. TheD _(FNLPδ) =D _(OHδ) +Δz _(G)  (49)elevation offset technique requires a measurement of elevation change,Δz_(G), between an OH point 362 and a FLP 364 with transmitter 264 atone position 366. Generally, this measurement will be performed onceearly in a drilling operation. With the drill head at position 366,FLP-depth, D_(FLPδ), (wherein δ indicates compensation for skin depth)can be calculated from the over head depth, D_(OHδ), and the measuredelevation change using:

Still referring to FIG. 15, the present technique is especially usefulfor a walk-over locator that is able to accurately measure over-the-headdepth accounting for skin effect, but is not configured for skin depthcompensation from the FLP. Since depth measured with such a locator at aforward locate point does not include skin effect, the ratioD_(FLPδ)/D_(FLP) obtained at transmitter position 366 can be employed tocorrect

$\begin{matrix}{D_{{FLP}\;\delta_{k}} = {\left( \frac{D_{{OH}\;\delta} + {\Delta\; z_{G}}}{D_{FLP}} \right)_{1}D_{{FLP}\; k}}} & (50)\end{matrix}$subsequent FLP depth measurements using the formula:

Here, the subscripts l and k denote the first and k-th locatingpositions respectively. It should be noted that this correction islinear and hence can only be expected to give accurate results for smalldepth variations and homogeneous soil properties.

Referring to FIG. 16, a dual point common elevation positiondetermination setup is generally indicated by the reference number 380.Accordingly, magnetic measurements are made at any two identifiablepoints having a common elevation. These measurements are combined toobtain transmitter depth in the presence of skin effects. It is assumedthat ground elevation changes only moderately between these two pointsso that the same locator elevation can be maintained by simply raisingor lowering the locator/detector unit relative to the surface of theground. This approach does not require an above ground calibration sinceskin depth is determined from magnetic field data together withtransmitter depth. Two such identifiable points are the OH and the FLPpoints, as indicated. At the OH location there is only a horizontalmagnetic flux B_(x) and at the forward locate point there is only avertical flux component B_(y). Even though transmitter 264 is shown in alevel orientation in this figure, its pitch is not required to be zero.The governing equations have already been described above for techniquesrelying on separate OH and FLP measurements. Specifically, equationsincluding (28) and (31) to (37) may be used for the solution oftransmitter depth D, skin depth δ and the variables r, ξ, η, λ, B_(ξ),B_(η), defined above. An example of a practical solution method can bederived by modifying the approach given previously for solving the setof equations (31) to (37). There the method requires the simultaneoussolution of the two nonlinear equations (42) and (43) for the geometricparameters λ and r. Here D, δ, λ and r are obtained by solving the 4nonlinear equations (28), (44), (45) and (46) simultaneously employingany standard numerical solution methods such as Newton's and functioniteration.

Referring once again to FIG. 7, multi-frequency transmitter 100 may beconfigured to transmit a locating signal at one or more carrierfrequencies and/or power levels consistent with the foregoingdisclosure. In addition to the reasons given above for varying the powerand frequency parameters described above, still further highlyadvantageous reasons for varying these parameters will be described atappropriate points hereinafter.

Still referring to FIG. 7, it is assumed for purposes of the presentexample that transmitter 100 is configured for transmission of thelocating signal at two different carrier frequencies. In this regard,calibration constants corresponding to these carrier locatingfrequencies, like any other locating frequencies, are measured andstored within calibration constants section 124. A number of provisionsmay be made for changing the locating frequency with the transmitterabove ground and, subsequently, during drilling. With regard to thelatter, as mentioned above, frequency of transmission may change ortoggle, for example, based on boring tool roll orientation sequence orroll rate. That is, the boring tool may be moved by means of the drillstring into a sequence of roll position orientations wherein the tool isheld stationary in each of the target roll orientations. Alternatively,a roll sequence may be employed rather than using actual rollorientation positions, as will be further described.

FIG. 17 illustrates one highly advantageous method for initiatinglocating frequency change during drilling using a roll orientationsequence generally indicated by the reference number 400. Initially,step 402 of method 400 reads a clock which forms part of microprocessor122. Step 404 then reads roll position as available, for example, fromaforedescribed roll/pitch sensor 112 (FIG. 7). In step 406, the rollposition and time of its recording are stored. The step 408 thencompares the roll position, as just read, to the roll position that wasrecorded responsive to steps 404 and 406 on the last loop of the processtherethrough, if available. If there is no change in roll position, theboring tool is not rotating such that step 410 is entered to set a stopflag. If, however, a change in roll position is indicated, step 412 isentered. This latter step tests for the roll rate. Specifically, if thechange in roll position is less than six clock positions a slow flag isset in step 414. If, on the other hand, the detected changing clockposition is greater than six clock positions, step 416 sets a fast flag.

After the execution of any of steps 410, 414, and 416, step 418 isexecuted, testing for a pattern match with reference to a saved ortarget roll sequence which may encompass positioning the boring tool atone or more stationary roll positions and/or rotating the boring tool atpredetermined rates for predetermined periods of time. Suitable rollsequences for use in initiating frequency change of the transmittershould encompass some roll sequence that is not normally performedduring typical drilling operations so as to avoid inadvertently togglingthe frequency of the locating signal.

One suitable roll sequence includes (i) stopping rotation of the boringtool for a time duration of approximately 7 to 20 seconds, (ii) rollingthe boring tool at a slow roll rate for a time duration of approximately7 to 20 seconds and (ii) without stopping, immediately going into a fastroll rate for approximately 7 to 20 seconds. The difference between thefast and slow roll rates may be defined by the drill rig that is in use.Generally, however, a slow roll rate is on the order of approximately 10to 30 rpm while a fast roll rate is greater than 30 rpm. Any definedfast and slow ranges of roll rate may be used so long as the ranges areseparated sufficiently to provide for distinguishing therebetween.

Another suitable roll sequence includes positioning the boring tool atthe roll positions of 4:00, 8:00 and 12:00 in three successive timeintervals, each of which is approximately 7-20 seconds in duration. Inthis regard, it should be appreciated that factors such as the length ofthe drill string should be considered with regard to the use of suchfixed roll orientations since “wrap-up” in a long string can, in somecases, cause difficulties in achieving a fixed roll position withprecision.

Continuing with a description of step 418 the detected pattern of rollto which the boring tool has been subjected is compared to the targetroll sequence that is used to initiate frequency toggling. In essence,the detected roll sequence or pattern is saved to allow microprocessor122 to look back in time for a period that is longer than the longestacceptable target roll sequence. Thus, in the present example, eachportion of the target roll sequence may be as long as twenty secondssuch that at least sixty seconds of roll information should be saved.This information may comprise the states of stop, slow and fast flagsrecorded by steps 410, 414 and 416, respectively, indexed against time.Where step 418 does not detect a pattern match, execution moves to step419 in which a frequency update is transmitted. This latter step isoptional, depending upon the specific implementation of the transmitter.It is advantageous where a roll/pitch carrier continuously transmitsdata such as, but not limited to, roll data, pitch data and depthcarrier frequency data on a frequency separate from the depth locatingsignal, as will be further described. Thereafter, operation returns tostep 402 in order to continue the monitoring process. When step 418 doesdetect a pattern match, step 420 initiates transmission of a newfrequency code which indicates to an above ground receiver that thetransmitter is about to change transmission frequencies. This step willbe described in further detail at appropriate points hereinafter. Instep 422, the transmitter toggles its transmission frequency. It isnoted for later reference that step 420 may be repeated one or moretimes immediately after performing step 422 depending upon theparticular implementation of the transmitter. The foregoing steps, likeall steps described throughout this disclosure, may be modified and/orvaried in sequence in any suitable manner within the context of aparticular implementation while remaining within the scope of thepresent invention.

As one alternative to subjecting the boring tool to a roll orientationsequence, signaling may be communicated to the boring tool using anisolated conductor carried within the drill string as described, forexample, in above incorporated U.S. patent application Ser. No.09/317,308 which is co-assigned with the present application.

Referring to FIG. 7, an ability to change the frequency of transmitter100 is required not just during drilling, but also with the transmitterabove ground, for example, to perform calibration procedures at each ofthe locating frequencies. The present invention contemplates a number ofhighly advantageous techniques for accomplishing frequency toggling withthe transmitter above ground. In this regard, such techniques are mostuseful when the frequency toggle may be accomplished with thetransmitter housed in the boring tool in its drilling configuration tofacilitate calibration accuracy. As will be seen, these above groundtechniques use reads of roll/pitch sensor 112 performed bymicroprocessor 122.

In one technique, the transmitter frequency is determined based upontransmitter pitch orientation on power-up of the transmitter. Forexample, when the transmitter is powered up having its forward end, asoriented toward the forward end of the boring tool when installedtherein, directed generally upward (preferably vertically upward), thetransmitter will begin transmitting at a higher one of the two availablelocating signal frequencies. When the transmitter is powered up havingits forward end directed generally downward (preferably verticallydownward), the transmitter will begin transmitting at a lower one of thetwo available locating signal frequencies. It should be appreciated thata pitch range within vertical at the time of power-up may be specifiedto initiate transmitting at either the low or high locating signalfrequency. One suitable pitch range is considered to be within 45degrees of a vertical orientation.

Another technique for accomplishing above ground toggling of transmitterfrequency uses a pitch orientation sequence. For purposes of such aboveground frequency toggling, the present invention recognizes that theboring tool may readily be subjected to pitch orientation sequences.Contemplated pitch orientation sequences are generally not possibleduring drilling. Like the aforedescribed roll sequences, a pitchorientation sequence is detected by using roll/pitch sensor 112. Onecontemplated pitch orientation sequence includes the step of initiallyplacing the transmitter in a horizontal orientation for a time period inthe range of approximately 7 to 20 seconds. The transmitter isthereafter placed in an approximately vertical orientation having theforward end of the transmitter pointing in a downward direction forapproximately 7 to 20 seconds. A concluding step places the transmitterback into the horizontal orientation again for approximately 7 to 20seconds. Responsive to exposure to this pitch orientation sequence, thetransmitter will respond by toggling its locating frequency. Specificprovisions relating to a receiver responsive to toggling of thetransmitter locating frequency will be described below. Still furtherabove ground frequency selection techniques may be developed within thescope of the present invention, particularly in view of the overallteachings herein.

With continuing reference to FIG. 7, data originating insensor/conditioning section 102, including roll and pitch, may betransmitted in any suitable manner using transmitter 100 such as, forexample, using tones that are modulated onto the locating signal. Inthis regard, Dual Tone Multi-Frequency (DTMF) encoding may be used. DTMFis discussed, for example, by U.S. Pat. No. 5,767,678 which isco-assigned with the present application and which is incorporatedherein by reference. As one alternative, frequency shift keying may beemployed. Control of divide by N counter, using microprocessor 122,provides for transmitting the data at any suitable frequency.Microprocessor 122 additionally executes any selected ones of theaforedescribed methods and techniques processes for toggling thetransmitting frequency of the locating signal by monitoring roll/pitchsensor 112. In one embodiment, the carrier frequency for this data alsoserves as the locating signal. As will be further described, asufficiently narrow band-pass filter (not shown) may be used within areceiver yet to be described to strip unwanted information from thecarrier frequency so as to insure accurate locating.

In another embodiment, additional components are provided as part ofreceiver 100 including a second divide by N counter 128 a which is alsocontrolled by microprocessor 122 (with control shown as passing throughdivide by N counter 128 a for purposes of simplicity). The output ofsecond divide by N counter 128 a serves as a depth locating signal,separate from the data carrier frequency. The depth locating signal isprovided to driver section 140 for mixing therein with the data carrierfrequency. The combined signals are then transmitted simultaneously fromantenna 146. Like the data carrier frequency, the depth locating signalis transmitted at any desired frequency, selectively separate from thefrequency of the data carrier frequency, and is switchable on-the-flybetween any frequencies within the range of divide by N counter 128. Thepresent example contemplates the use of two frequencies comprising a lowdepth frequency of 1,516 Hz and a high depth frequency of 32,766 Hz forreasons to be described below. For the moment, it is appropriate to notethat this embodiment is generally advantageous with the use of the 1,516Hz depth locating signal since the data carrier frequency may remain ata higher value. That is, the low depth frequency may be sufficientlylow, in this instance, so as to adversely limit available bandwidth forpurposes of data transmission. It should be appreciated that transmitterof the present invention is not limited to the exemplary embodimentdescribed, but may be implemented in any number of alternative wayswhile remaining within the scope of the invention.

Having described the transmitter of the present invention, attention isnow directed to additional advantages associated with the ability totransmit at two or more locating depth frequencies and, moreparticularly, to the advantages associated with the ability to transmitat a low depth frequency and a high depth frequency. One problemcommonly encountered during drilling and locating operations relates tonoise. Such noise may emanate, for example, from traffic loops and fromother directional drilling and/or cable locating operations. It istherefore advantageous, in many instances, to change the locating signalto one or the other of the possible locating frequencies which is lesssusceptible to the particular noise that is being encountered within thedrilling region. Another problem has been found to stem from thepresence of metal reinforcing bar present, for example, within concretestructures or roadbeds within the drilling region. The capability to usea relatively low locating frequency is advantageous in this particularsituation because induced currents in the reinforcing bar increase inproportion to the locating frequency. At the low 1,516 Hz frequencycontemplated for use herein, actual testing reveals a virtual absence ofinterference effects even with the presence of a considerable amount ofreinforcing bar.

Turning to FIG. 18 in conjunction with FIG. 7, a highly advantageousdual frequency receiver, produced in accordance with the presentinvention, is generally indicated by the reference number 450. Thelatter includes first and second orthogonally arranged antennasindicated by the reference numbers 452 a and 452 b, respectively. A fourpole double throw relay includes four sets of contacts indicated by thereference numbers 454 a-d that are controlled by a microprocessor 456.Antenna 452 a is connected to the pole of contact set 454 a whileantenna 452 b is connected to the pole of contact set 454 c. With therelay contacts closed in the upper position, as illustrated, receiver450 is configured for reception of the low depth frequency such that thereceived locating signal on each of antennas 452 a and 452 b is coupledinto mixer A and mixer B, respectively. Each mixer additionally receivesa mixing frequency produced by a local oscillator 458. In the presentexample, the local oscillator frequency is set to 31,250 Hz. The lattermixes with the received 1,516 Hz low depth frequency to produce anoutput frequency of 32,766 Hz at the output of each mixer. Relay contactsets 454 b and 454 d direct the mixed signals to a first depth receiverDR1 and a second depth receiver DR2, respectively. The depth receiversperform appropriate signal processing such as, for example, filteringand amplification. The processed signals are then transferred to amultiplexer 460. The analog multiplexed signals originating from thefirst and second depth receivers are converted to digital form using ananalog to digital converter 462. The digitized depth signals are thenreceived by microprocessor 454.

At the same time, a roll/pitch antenna 464 receives the roll/pitchcarrier for use by a roll/pitch receiver 466. In one embodiment, theroll/pitch carrier may remain at approximately the same frequency as thehigh depth frequency, 32,766 Hz, independent of the depth locatingfrequency. The roll/pitch receiver recovers available boring tool dataincluding, but not limited to roll, pitch, temperature, battery statusand any other suitable information transmitted for presentation tomicroprocessor 454. In another embodiment, the roll/pitch carrier maycomprise whichever depth frequency is being transmitted. That is, theroll/pitch data is encoded upon and accompanies the depth carrierfrequency. In this instance, an additional mixer is provided toheterodyne the low depth frequency up to the high depth frequency usingoscillator 458 and a relay connection arrangement. This arrangement andthe additional mixer have not been illustrated since it appearsessentially the same as the arrangements described above associated withthe high and low depth frequencies. Further details regarding theseembodiments will be provided below.

Receiver 450 is configured for operation in one of two selectable modeswith respect to reception of the locating signal at a selected one oftwo or more frequencies—a manual mode and an automatic mode. Thesechoices are presented to the operator during power-up sequencing. In themanual mode, the operator selects the locating signal frequency from aset of available frequencies. The receiver is then forced to receive atthat frequency irrespective of which frequency is in actual use. Thisfeature is advantage, for example, where two drill rigs are operating inthe same region. In the automatic mode, which is also selectable by theoperator, the receiver searches for the locating frequency in use andremains at that frequency. In embodiments where the roll/pitch data istransmitted via a carrier that is separate from the depth locatingsignal, the receiver is responsive to periodic frequency updateinformation that is encoded along with other data on the roll/pitchcarrier, which updates may be transmitted from the boring tool, forexample, in accordance with method 400 of FIG. 17. It should be notedthat a single bit in the encoded data may be used as a command or codeto indicate the selected depth carrier frequency where two depthfrequencies are available. In this way, the receiver is able to find thelocating signal by merely reading the relevant data and is dynamicallyresponsive when the locating frequency toggles. In embodiments where theencoded frequency is encoded on the depth carrier signal to change infrequency therewith, one or more frequency updates are transmitted bythe boring tool prior to switching frequencies such that the receiver isdynamically responsive to frequency toggling.

Another feature provided by receiver 450 relates to the way in which thereceiver powers up. In particular, the receiver powers up at the samelocating signal frequency at which it was last powered down. Such apower-up frequency feature is highly advantageous in a number ofoperational scenarios particularly where the frequency data is encodedon the depth locating signal. For example, if the receiver is turned offduring a lunch break, drilling operations may resume without the need toverify that the receiver is on the correct locating frequency. Asanother example, in a situation where the operator uses the manual modeto force the receiver to receive at a particular depth carrier frequencyin a region where two drill rigs are operating, it is assured that theoperator will resume tracking the correct locating signal. In thisregard, a receiver configured to always revert to one particular depthcarrier frequency at power-up is considered as being unacceptable. Thepower-up frequency feature of the present invention may readily beimplemented in a power up/down routine using microprocessor 454 by onehaving ordinary skill in the art in view of this overall disclosure.Moreover, the design of receiver 450 may be modified in any suitablemanner while remaining within the scope of the present invention so longas the teachings herein are applied.

Attention is now directed to FIG. 19 which illustrates roll/pitchreceiver 466 of FIG. 18 in block diagram form. A tuned amplifier 470 isconnected to roll/pitch antenna 464 for receiving the roll pitch carrierfrequency which is essentially an analog signal or stream having encodeddigital information. Again, an additional mixer and extension of therelay switching arrangement have not been illustrated since the additionof these components is within the capabilities of one having ordinaryskill in the art. Tuned amplifier 470 is tuned sufficiently narrow so asto eliminate noise outside the frequency range of interest. As mentionedabove, data may be encoded, for example, using tones. In oneimplementation, the tones may be encoded at one or more frequenciesbelow 1 kHz. The present example contemplates the use of two differenttones which are transmitted for a predetermined interval that is termeda “bit time”, as will be seen.

Still referring to FIG. 19, roll pitch receiver 466 includes a mixer 472and a local oscillator 474. The latter may be replaced, if so desired,by a tuning arrangement (not shown) including an oscillator and a divideby N counter reflecting the configuration previously described withregard to receiver 100 of FIG. 7 in implementations which utilize two ormore roll/pitch carrier frequencies. In such implementations, the tuningarrangement as well as tuned amplifier 470 may be under microprocessorcontrol. Local oscillator 474 operates at a frequency which is selectedso as to mix the data tones down to a base band frequency range torecover the tones at their original frequencies. A band pass filter 476strips away extraneous noise. The tones are then amplified using anamplifier 478. In accordance with the present invention, a comparator480 converts the analog tone data into binary digital data by comparingthe incoming information to a switching threshold. Thereafter, thebinary tone data is received by a highly advantageous tone detectionarrangement 482 which is indicated within a dashed line. Tone detectionarrangement 482 itself includes first and second microcontrollersselected, for example, from the PIC series of microcontrollers that areavailable from Microchip and which are indicated as PIC1 and PIC2. Thesemicrocontrollers utilize a RISC (Reduced Instruction Set Architecture).In essence, a bare minimum set of instructions is provided. Thesemicrocontrollers, in turn, interface with a supplemental microprocessor486. The latter outputs data to main microprocessor 454 on a line 488,shown in FIG. 18. Specific details regarding the operation of tonedetection arrangement 482 will be provided immediately hereinafter.

Each microcontroller (PICs 1 and 2) is configured for detecting asingle, “target” tone. Thus, two microcontrollers are provided in thepresent example. The incoming data is sampled at a predetermined ratebased on the target tone. The amplitude, F, of a particular frequencymay be represented using an in-phase component, I, and a quadraturecomponent, Q where:|F|=√{square root over (I² +Q ²)}  (51)Where F represents the magnitude of a time dependent function. It isnoted that phase information may be obtained based on the ratio of Iover Q. Components I and Q may be represented by the integrals:I=∫F(t)cos(ωt)dt, and  (52)Q=∫F(t)cos(ωt)dt.  (53)

A match filter configuration is used in a highly advantageous manner forevaluating I and Q. Specifically, the foregoing integrals areapproximated by evaluation at every 90° interval equating to foursamples per cycle of the “target” tone. In other words, a sample istaken every ¼ cycle. A plurality of samples is taken over a samplingperiod, which is based, for example, on the anticipated time duration ofthe target tone. It will be appreciated that a match filter essentiallydetermines the coefficient or amplitude of a particular frequency ofinterest consistent with an abbreviated form of Fourier transform. Thevalues of the sine and cosine functions at 90° intervals are given byTable 1.

TABLE 1 Cosine and Sine Function Values per 90° Intervals Function 0°90° 180° 270° cos ωt 1 0 −1 0 sin ωt 0 1 0 −1

Based on the foregoing, the approximation ignores F(t)cos ωt at ωt=90°and 270°, since cos ωt=0. Further, the approximation ignores F(t)sin ωtat ωt=0° and 180°, since sin ωt=0. The value of I is thereforecontributed to at ωt=0° and 180° while the value of Q is contributedωt=90° and 270°. In this regard, it is important to understand thatcomparator 480 converts the incoming data to binary form based on asingle threshold. The value of the data, F(t) at any one point in timeis, therefore, a binary zero (0) or a binary one (1). Accordingly, thedetermined value of the approximation is either a 0 or 1, based on theincoming data, which is multiplied by a 1 or −1, based on thecorresponding value of cos ωt or sin ωt. Table 2 illustrates the outputvalue for each of I and Q based on the various input parameters. An “X”in the I and Q columns denotes an ignored value. That is, there is noneed to determine a value for that particular combination of inputparameters for the indicated I or Q value since either cos ωt or sin ωtcontrols by being equal to zero. For descriptive purposes, the Iapproximation may be considered as being evaluated at odd numberedsample intervals while the Q approximation may be considered as beingevaluated at even numbered sample intervals.

TABLE 2 Match Filter Definition ωt cos ωt sin ωt Input Data I Q  0° 1 00 0 X  90° 0 1 0 X 0 180° −1 0 0 0 X 270° 0 −1 0 X 0  0° 1 0 1 1 X  90°0 1 1 X 1 180° −1 0 1 −1  X 270° 0 −1 1 X −1 

It should be appreciated that the match filter of the present inventioneffectively serves to eliminate the need for multiplication, rather theinclusion of a minus sign is simply required at the appropriate timesseen in Table 2. Moreover, a number of complex mathematical operationsare eliminated, at least including the need to actually evaluate thesine and cosine functions. Still further advantages will be describedbelow.

Turning now to FIG. 20, having described the approximation used in thematch filter of the present invention, specific details with regard toits implementation in the PIC microcontrollers will now be describedwith reference to a match filter method that is generally indicated bythe reference number 500. It is noted that each of the values of I and Qis stored in a respective accumulator or memory location (not shown).Method 500 begins with a start step 502 and proceeds to step 504 inwhich a number of values denoted as “Samples”, I and Q are set to 0. CNTis set to 1. Samples represents a running total of the number of samplestaken by the filter while CNT is a counter value. Step 506 then readsthe binary data input value. Step 508 then increments Samples.Thereafter, step 510 tests the value of CNT, if it is not equal to 1,step 512 is next performed, as will be described. If, on the other hand,CNT is equal to 1, step 514 is performed. This latter step tests thebinary data input value. If the input is 1, step 516 is performed whichincrements I by one unit. If the input value is 0, step 516 is notperformed. Following either case, step 518 increments the value of CNTby 1. In the present example, CNT now is equal to 2.

Following Step 518, step 520 introduces a ¼ cycle delay which coincideswith ¼ of the cycle time of the target tone being detected by thisparticular filter. The filter is therefore advantageously adaptable tothe detection of any target tone through the simple expedient ofadjusting the delay introduced by step 520. In step 522, the value ofSamples is compared to the bit time. In other words, some predeterminednumber of samples are taken over successive bit times. If Samples isequal to the bit time, step 524 causes the filter to provide anapproximate output magnitude, as will be further described. Executionthen moves back to step 504, to set up for monitoring over the next bittime. If Samples is less than the bit time, execution moves from step522 directly back to step 506.

Returning to the discussion of step 512, with CNT=2 on the second loopthrough process 500, step 510 passes execution to step 512. The lattercompares CNT to the value 2. If the value of CNT is not equal to 2, step526 is performed, as will be described. If the value of CNT is equal to2, step 528 is performed to test the binary data input value. If theinput is 1, step 530 is performed which increments Q by one unit. If theinput binary value is 0, step 530 is not performed. In any case, step518 then increments the value of CNT by 1. In the present example, CNTnow is equal to 3. Execution continues with steps 520 and 522 returningto either step 504 or 506 dependent upon the outcome of step 522. In thepresent example, it is assumed that Samples is less than the bit timesuch that processing returns to step 506.

On the third loop through process 500 with CNT=3, step 506 reads thebinary value anew and step 508 increments Samples. Step 510 passesoperation to step 512 which, in turn, passes operation to step 526. Ifthe value of CNT is not equal to 3, step 532 is performed, as will bedescribed. If the value of CNT is equal to 3, step 534 is performed totest the binary data input value. If the input is 1, step 536 isperformed which decrements I by one unit. If the input binary value is0, step 530 is not performed. Thereafter, step 518 then increments thevalue of CNT by 1. In the present example, CNT now is equal to 4.Execution continues with steps 520 and 522 returning to either step 504or 506 dependent upon the outcome of step 522. In the present example,it is assumed that Samples remains less than the bit time such thatprocessing returns to step 506.

On the fourth loop through process 500 with CNT=4, step 506 once againreads the binary data value and step 508 increments Samples. Step 510passes operation to step 512 which, in turn, passes operation to step526 and then to step 532. The latter resets CNT to 0. Step 538 thentests the binary data input value. If the input is 1, step 536 isperformed which decrements Q by one unit. If the input binary value is0, step 530 is not performed. Thereafter, step 518 then increments thevalue of CNT by 1 such that CNT=1. Execution continues with steps 520and 522 returning to either step 504 or 506 dependent upon the outcomeof step 522. The process will repeat beginning with step 504, onceSample is equal to the bit time at step 522.

It should be appreciated that step 524 is performed at the conclusion ofeach sampling duration which is generally set to one bit time.Accordingly, an accumulated value is associated with each of I and Q, asdetermined over the number of samples associated with each bit time.Method 500 is highly advantageous in that only simple arithmeticoperations are needed. That is, increment by one unit and decrement byone unit. Alternatively, the accumulator value is simply maintained. Themagnitude of the target tone may be determined in a number of differentways such as, for example, using equation 51 with the established valuesof I and Q. In this regard, however, it should be appreciated thatequation 51 requires the use of several relatively complex mathematicaloperations including squaring and square root. As will be seen, thepresent invention provides a highly advantageous magnitude estimationmethod which does not rely on such complex mathematical functions whilemaintaining sufficient accuracy, as will be described immediatelyhereinafter. It should be appreciated that the roll/pitch receiver maybe implemented in an unlimited number of ways while remaining within thescope of the present invention. For example, the use of PICmicrocontrollers is not required by implementing the receiver of thepresent invention with a single microprocessor. Moreover, it isconsidered that the steps which make up method 500 may be modified orpracticed in many other different, but suitable orders while remainingwith the scope of the present invention.

Attention is now directed to FIG. 21 which illustrates a Q-I coordinateaxis generally illustrated by the reference number 550. The equationI²+Q²=V² is plotted on the coordinate axis wherein V represents ascaling constant. The semi-circular plot corresponding to this equationrepresents the locus of points for the exact value of the magnitude ofthe determined tone, in accordance with equation 51. The magnitude isdetermined by the present invention using a three line approximation.The three lines used in the magnitude estimation are I=V, I=Q andI=√{square root over (2)}V−Q. As shown in the figure, each line forms asegment that is tangent to I²+Q²=V² for use in the approximation. Whilethis approximation, in and by itself, provides acceptable accuracy, ithas been found that accuracy is still further enhanced by using thelines:

$\begin{matrix}{{I = {KV}},} & (54) \\{{Q = {KV}},{and}} & (55) \\{I = {{\left\lbrack {\sqrt{2} - \frac{1 - K}{\sqrt{2}}} \right\rbrack V} - Q}} & (56)\end{matrix}$where K is a constant. One useful value for K has been found to be0.974. Using this value, FIG. 21 shows dashed lines representing theseline segments. Each is shifted just slightly toward the origin so as tooverlay and intersect the I²+Q²=V² circle. Using the approximation withthis accuracy enhancement and K=0.974, an error of no more than 6% isachieved. The specific manner in which this curve fit is used by setoutput step 524 of FIG. 20 using each PIC microcontroller will bedescribed immediately below.

Referring to FIGS. 20 and 21, it should be appreciated that V may beconsidered to represent a threshold at or above which a tone is present.Accordingly, the three segment curve fit is performed by testing theinequality I≧V. If satisfied, step 524 indicates the presence of thetarget tone. Otherwise, the inequality Q≧V is tested. If this latterinequality is satisfied, step 524 indicates the presence of the targettone. In the event that neither of the first two inequalities issatisfied, the inequality I+Q≧√{square root over (2 )}V is tested. Ifsatisfied, step 524 indicates the presence of the tone. In the eventthat none of the inequalities is satisfied, the tone is indicated asbeing absent. Of course, these curve fit inequalities are readilyadapted to accommodate enhanced accuracy in view of equations 54-56 byreplacing the equals sign with a greater than or equal to sign. The useof two or more tones will be considered immediately hereinafter.

Referring to FIGS. 19-21, where two or more tones may be present, it isadvantageous to provide discrimination therebetween. In this case, itmay be preferable to normalize the accumulated values of I and Q againstthe total number of samples taken in a bit time since bit times fordifferent tones may include different numbers of samples. FIG. 19illustrates that each PIC microcontroller provides its tone indicationoutput to microprocessor 486 via two data lines. Accordingly, theabsence of a tone may be indicated as 0,0 on these lines. The threeremaining signaling combinations (0,1; 1,0 and 1,1) represent increasingrelative magnitude of the tone. These three relative magnitudescorrespond to three different values of V, as used in the inequalitiesof the curve fit approximation. That is, the curve fit is repeated usinga set of magnitude thresholds: V₁, V₂ and V₃ where V₁<V₂<V₃. It shouldbe appreciated that any number of thresholds may be used dependant on aparticular implementation. In instances where two or more tones areindicated as having the same magnitude, a priority mechanism may beinvoked whereby the tone which occurs most often out of the tones whichmake up the tie is indicated as being present. In an actualimplementation, having I and Q normalized to the range 0-1, the values0.50, 0.56 and 0.62 were used for V₁, V₂ and V₃, respectively.

Turning to FIGS. 19 and 20, it is important to understand that method500 represents the implementation of a single match filter. As will beseen, each of the PIC controllers in FIG. 19 executes a plurality ofindividual ones of these highly advantageous digital match filterssimultaneously.

Referring to FIG. 22, the simultaneous operation of a plurality ofdigital match filters within one of the PIC controllers of FIG. 19 isdiagrammatically illustrated. Operation is shown over a time periodcomprising three bit times which are individually indicated as BT0, BT1and BT2. An input data plot illustrates the incoming binary data asreceived by the PIC controller. A tone 604 is present within the binarydata throughout BT1. The frequency of the tone has not been shown toscale for illustrative purposes. It should be remembered that eachfilter operates for the duration of one bit time at the conclusion ofwhich step 524 provides an output for that filter. The filter,thereafter, immediately begins sampling over the next bit time.Moreover, no synchronization is required between the start times of thevarious filters and the actual bit times seen in the incoming data. Sucha synchronized relationship has been illustrated here only for purposesof simplifying the present description in order to aid the reader'sunderstanding.

Still referring to FIG. 22, filter sampling times are illustrated foreach of eight individual filters implemented within the PICmicrocontroller. Individual ones of the filters are indicated as f1-f8.While eight filters are illustrated in the present example, it should beappreciated that the total number of filters implemented within any onemicrocontroller is dependent upon the processing capabilities of theparticular microcontroller in use. As the number of implemented filtersis increased, accuracy in the detection of tone edges is improvedcorrespondingly. Filters f1-f8 are initialized at staggered timeincrements corresponding to ⅛ of a bit time, beginning withinitialization of f1 at the beginning of BT0. Therefore, f1 provides anoutput for a duration of ⅛ of a bit time immediately following BT0. Thisoutput is illustrated in a filter output plot indicated by the referencenumber 610. The filter output plot is normalized for purposes of clarityshown from 0 to 1 along a vertical axis 611. A time line 612 immediatelybelow the filter output plot labels ⅛ bit time increments 1-17 fordescriptive purposes. Further, below that, the filter providing theindicated output for that increment is denoted. It can be seen that theoutput of f1 corresponding to BT0 is zero during time increment 0, sincef1 saw none of tone 600.

Filter f2 starts ⅛ of a bit time following the start of filter f1 andcompletes sampling for one bit time with the conclusion of timeincrement 1. Thus, filter f2 samples during ⅛ of the total duration (onebit time) of tone 604. The corresponding output of filter f2 is ⅛(0.125) during time increment 2. Each successive filter samples over anadditional ⅛ of the duration of tone 604. For this reason, the filteroutput plot steps incrementally up by ⅛ with the output of eachsuccessive filter. For example, filter f7 outputs 6/8 (0.75) during timeincrement 7 while filter f8 outputs ⅞ (0.875) during time increment 8.

With continuing reference to FIG. 22, each filter restarts immediatelyupon completing sampling for a duration corresponding to one bit time,even as its output is being determined and provided. Thus, filter f1restarts at the beginning of time increment 1 and concludes sampling forthe duration of one bit time with the conclusion of time increment 8.The output during time increment 9 is then responsive to the valuedetermined using filter f1 sampling over BT1. Therefore, the outputvalue seen in output waveform plot 610 is 1.0 during time increment 9.

At time increment 9, filter f1 restarts for a second time, providing anoutput during time increment 17. Since the f1 filter samples over BT2,during which no tone is present in the input binary data, the outputduring time increment 17 is zero.

The filtering process continues with each of filters f2-f8 restartingwith successive ⅛ bit time increments. In this instance, however, eachsuccessive starting filter sees ⅛ less of tone 604. For example, theoutput corresponding to the restart of filter f2 is present during timeincrement 10 and has a value of ⅞ (0.875). The outputs corresponding tothe restart of filters f3-f8 are present during time increments 11-16,respectively, having values decreasing by ⅛ with each successive filteroutput. Thus, filter output plot 610 has stepped up in value from 0.0 upto 1.0 and then stepped down in value back to 0.0. If tone 604 ispresent during alternating ones of the bit times (partially shown),filter output plot 610 approximates a triangular waveform. The filtersoperate continuously in a staggered time relation to one another. Itshould be appreciated that the filter output plot crosses the value 0.5at time increments 5 and 13, corresponding to one bit time. If the valueof V, as described above, is set to a threshold of 0.5 the combinedoutputs of the filters will indicate the presence of tone 604 with assignificant degree of accuracy, delayed by one-half of one bit time. Theeffect of using increasing numbers of filters resides in a smootherappearing triangular waveform (not shown). For example, if 16 filtersare used, the vertical steps in the filter output plot are 1/16, asopposed to ⅛, while the time increments shown in time line 612 arereduced in duration by one-half.

Having described the highly advantageous roll/pitch receiver and digitalmatch filter of the present invention, it is appropriate to draw acomparison with the prior art. The approach taken in the prior art hasgenerally been digitization of incoming data using an analog to digitalconverter such that the digitized data represents a plurality ofdiscrete magnitude values responsive to the incoming data. The data istypically processed using a digital signal processor invoking ratherintensive and complex computations such as, for example, Fast FourierTransform. The present invention, in contrast, provides a far lesscomputationally complex approach which yet remains highly effective. Inthis regard, it is important to understand that the digital match filterand tone detection arrangement of the present invention enjoy wideapplication and are in no way limited to use in drilling systems.

In that skin depth compensation arrangements, multi-frequencytransmitters, multi-frequency receivers and associated methods disclosedherein may be provided in a variety of different configurations andmodified in an unlimited number of different ways, it should beunderstood that the present invention may be embodied in many otherspecific forms without departing from the spirit of scope of theinvention. Therefore, the present examples and methods are to beconsidered as illustrative and not restrictive, and the invention is notto be limited to the details given herein, but may be modified withinthe scope of the appended claims.

1. In an overall method of operating a system in which a transmitter ismoved through the ground in a region which includes an electricalconductivity characteristic, said system including an above groundarrangement for tracking the position of and/or guiding the transmitteras the transmitter moves through the ground, said transmitter beingconfigured for transmitting a locating signal for reception by saidabove ground arrangement in said region for measurement of the locatingsignal by the above ground arrangement, the improvement comprising:compensating for skin depth error by measuring said locating signal suchthat measurements of the locating signal include skin depth errorintroduced as a result of said electrical conductivity characteristicand, thereafter, using said measurements in a way which determines askin depth corrected position of the transmitter.
 2. The improvement ofclaim 1 wherein said measurements are produced by (i) transmitting thelocating signal from the transmitter to said arrangement at apreselected number of different frequencies such that each frequencypenetrates said region with a different skin depth, and (ii) measuringan intensity of the locating signal at each frequency to provide anumber of intensity measurements corresponding to the preselected numberof said different frequencies, and wherein the skin depth correctedposition of the transmitter is determined by using said intensitymeasurements in combination.
 3. The improvement of claim 2 whereindetermining the position of the transmitter using said intensitymeasurements includes the steps of (i) developing a set of magneticintensity equations such that one equation corresponds to each frequencyfor use with one of the intensity measurements, said equations includinga number of coefficients in frequency equal to the number of intensitymeasurements such that one of the coefficients is a constant whichrepresents a steady state electromagnetic value of the locating signal,(ii) solving for said coefficients including the constant coefficientand (iii) using said constant coefficient as an electromagnetic readingat zero frequency to determine the position of the transmitter relativeto said arrangement at zero frequency such the effect of skin depth issubstantially reduced.
 4. The improvement of claim 1 wherein certainones of said measurements are used to determine a value for skin depthto be used during the determination of the skin depth corrected positionof the transmitter, these certain measurements being obtained in acalibration procedure by transmitting the locating signal from thetransmitter to said arrangement.
 5. In a system in which a transmitteris moved through the ground in a region which includes an electricalconductivity characteristic, said system including an above groundarrangement for tracking the position of and/or guiding the transmitteras it moves through the ground using a locating signal that istransmitted from the transmitter and for reception by said above groundarrangement such that the electrical conductivity of said region resultsin a skin depth which modifies penetration of the locating signal intosaid region and, consequently, which produces skin depth error when oneor more measurements of the locating signal are used, as measured by theabove ground arrangement and influenced by skin depth, to determine thelocation of the transmitter relative to said above ground arrangementunder an assumption that said region is electrically non-conductive, anapparatus comprising: a compensation arrangement forming part of saidtransmitter and/or part of said above ground arrangement forcompensating for skin depth error based on said measurements of saidlocating signal such that a skin depth corrected position of thetransmitter is established.